There are some cases where LabelEncoder or DictVectorizor are useful, but these are quite limited in my opinion due to ordinality.

LabelEncoder can turn [dog,cat,dog,mouse,cat] into [1,2,1,3,2], but then the imposed ordinality means that the average of dog and mouse is cat. Still there are algorithms like decision trees and random forests that can work with categorical variables just fine and LabelEncoder can be used to store values using less disk space.

One-Hot-Encoding has the advantage that the result is binary rather than ordinal and that everything sits in an orthogonal vector space. The disadvantage is that for high cardinality, the feature space can really blow up quickly and you start fighting with the curse of dimensionality. In these cases, I typically employ one-hot-encoding followed by PCA for dimensionality reduction. I find that the judicious combination of one-hot plus PCA can seldom be beat by other encoding schemes. PCA finds the linear overlap, so will naturally tend to group similar features into the same feature.

Label encoding imposes artificial order: if you label-encode your pet target as 'Dog':0, 'Cat':1, 'Turtle':2, 'Golden Fish':3, then you get the awkward situation where 'Dog' < 'Cat' and 'Turtle is the average of 'Cat' + 'Golden Fish'.

In the case of predictor features (not the target), this is a problem since your Random Forest can be learning something like "if it less than 'Turtle', then...".

Also, you may have categories in the testing set (or even worse, new data during deployment) that were not present in the training, and the transformer doesn't know what to do, so it throws an error. This may be the case or not depending on the particular problem and particular feature you are encoding, obviously not for the target variable.

When hot encoding, if a category absent in the training is present in a prediction, it just get encoded as 0 in each of the encoded features (new columns representing each category), so you don't get an error. Your model still has the other features to make a reasonable guess.

As a general rule, you want to use label encoding for target variables and OHE for predictor features. Note that in general you don't care about artificial order in the target, since the prediction is usually categorical also (A forest will choose a number, not a range of numbers; a network will have one activation unit per category...)

I don't think optimization should be part of the discussion here since they are used for different scenarios demanding different outputs: surely it's more efficient to use the OHE transformer than trying to hack it by performing label encoding and then some pandas trickery to create the same result as with one hot encoding.

Here there are useful comments about the different scenarios (type of model, type of data) and some issues related to efficiency.

Here there's an example on why label encoding is a bad practice for input features.

And let's not forget that the goal of the model is to make predictions, so at the end what's important is not just the output of <transformer>.fit_transform, but also the fitted transformer itself that's going to be applied to the new observations. OHE will deal with new cases differently than label-encoder (e.g. when the value of the feature in the observation was not present in the training set). That's in my opinion enough reason to have different methods, even when they act in a way similar enough so, for some inputs, you may be able to force them to give similar outputs.

A simple example which encodes an array using LabelEncoder, OneHotEncoder, LabelBinarizer is shown below.

I see that OneHotEncoder needs data in integer encoded form first to convert into its respective encoding which is not required in the case of LabelBinarizer.

from numpy import array
from sklearn.preprocessing import LabelEncoder
from sklearn.preprocessing import OneHotEncoder
from sklearn.preprocessing import LabelBinarizer

# define example
data = ['cold', 'cold', 'warm', 'cold', 'hot', 'hot', 'warm', 'cold', 
'warm', 'hot']
values = array(data)
print "Data: ", values
# integer encode
label_encoder = LabelEncoder()
integer_encoded = label_encoder.fit_transform(values)
print "Label Encoder:" ,integer_encoded

# onehot encode
onehot_encoder = OneHotEncoder(sparse=False)
integer_encoded = integer_encoded.reshape(len(integer_encoded), 1)
onehot_encoded = onehot_encoder.fit_transform(integer_encoded)
print "OneHot Encoder:", onehot_encoded

#Binary encode
lb = LabelBinarizer()
print "Label Binarizer:", lb.fit_transform(values)

Another good link which explains the OneHotEncoder is: Explain onehotencoder using python

There may be other valid differences between the two which experts can probably explain.